Option Contracts

Chapter 24

Innovative Financial InstrumentsDr. A. DeMaskey

Derivatives

Forwards– fix the price or rate of an underlying asset

Options– allow holders to decide at a later date whether

such fixing is in their best interest

Option Market Convention

Private transactions (OTC)– asset illiquid– credit risk is one-sided– created in response to needs– associations of broker-dealers

Chicago Board Options Exchange (CBOE)– Options Clearing Corporation (OCC)

Price Quotations for Exchange-Traded Options

Equity options– CBOE, AMEX, PHLX, PSE– typical contract for 100 shares– require secondary transaction if exercised– time premium affects pricing

Price Quotations for Exchange-Traded Options

Stock index options– only settle in cash

Foreign currency options– allow sale or purchase of a set amount of non-USD

currency at a fixed exchange rate– quotes in USD

Options on futures contracts (futures options)– right, but not the obligation, to enter into a futures

contract at a later date at a predetermined price

The Fundamentals of Option Valuation

Risk reduction tools when used as a hedge– Theoretical value of option depends on combining it

with its underlying security to create a synthetic riskfree portfolio.

– Theoretically, it is always possible to use the option as a perfect hedge against fluctuations in the value of the underlying asset.

Put-Call Parity versus Option Valuation

The portfolio implied by the put-call parity transaction does not require special calibration.

Put-call parity paradigm does not require a forecast of the future price level of the underlying asset.

Basic Approach

Create a riskless hedge portfolio by combining options with the underlying security.

– Hold one share of stock long and some number of call options so that the position is riskless.

– Number of call options (h) needed is established by ensuring portfolio has same value at expiration regardless of forecasted stock values.

Solve for hedge ratio, h, which has both direction and magnitude.

Assume no arbitrage opportunities exit, so that the value of the hedge portfolio should grow at the riskfree rate.

Improving Forecast Accuracy

Subdivide interval into subintervals, and form a stock price tree

Work backward on each pair of possible outcomes from the future

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The Black-Scholes Valuation Model

For a European call option on a non-dividend paying stock, Black and Scholes developed the following:

The Black-Scholes Valuation Model

Value is a function of five variables:– Current security price– Exercise price– Time to expiration– Riskfree rate– Security price volatility

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Estimating Volatility

Mean and standard deviation of a series of price relatives:

Problems With Black-Scholes Valuation

Stock prices do not change continuously. Arbitrageable differences between option

values and prices (due to brokerage fees, bid-ask spreads, and inflexible position sizes).

Riskfree rate and volatility levels do not remain constant until the expiration date.

Option Valuation: Extensions and Advanced

Topics Valuing European-style put options Valuing options on dividend bearing

securities Valuing American-style options Stock index options Foreign currency options Futures options

Exotic Options Asian options

– Terminal payoff determined by the average price of the underlying security during the life of the contract.

– Payoff = max [0, Average(S) - X] Lookback options

– Terminal payoff based on the maximum price of the underlying security achieved during the life of the contract.

– Payoff = max [0, max(S) - X] Digital options

– Terminal payoff is fixed.– Payoff = $Q if ST > 0 or $0 if ST < 0

Option Trading Strategies

Protective put options Covered call options Straddles, strips, and

straps

Strangle Chooser options Spreads Range forwards

Protective Put Options

Purchase at-the-money put to hedge against a fall in the price of a stock already held

(Long Stock) + (Long Put) = (Long Call) + (Long T-Bill)

– Insures position in equity– Preserves potential for capital gains if stock

price rises, but limits loss if stock price falls

Covered Call Option

Sale of a call option while owning the stock

(Long Stock) + (Short Call) = (Long T-Bill) + (Short Put)

– Generates income from premiums– Risks:

• Stock may be called away if price rises• Price of stock my decline by more then premium

received

Straddles, Strips, and Straps

Straddle– Simultaneous purchase (or sale) of a call and a put with the same

underlying asset, exercise price, and expiration date– Buyer expects price to move a lot up or down– Seller expects price to remain fairly stable

Long Strap– Purchase of two calls and one put with the same exercise price– Buyer expects price increase is more likely

Long Strip– Purchase of two puts and one call with the same exercise price– Buyer expects price decrease is more likely

Strangle

Simultaneous purchase or sale of a call and a put on the same underlying security with the same expiration date, but whose exercise prices are both out-of-the money.– Reduces initial cost– Price will have to move more for a profit– Modest risk-reward structure

Chooser Options

Investor selects exercise price and expiration date, but decides after the purchase whether the option is a put or a call.

This is an option with an embedded option that is more expensive.

Spreads

Purchase of one contract and the sale of another, in which the options are alike in all respects except for one distinguishing characteristic.

Money Spread– Sell an out-of-the money call and buy an in-the-money

call on the same stock with the same expiration date. Calendar Spread

– Purchase and sale of two calls (or two puts) with the same exercise price but different expiration dates.

Spreads

Bull Spread– Buy an in-the-money call and sell an out-of-the money call– Profitable when stock prices rise

Bear Spread– Buy and out-of-the-money call and sell an in-the-money call– Profitable when stock prices fall

Butterfly Spread– Combining a bull money spread and a bear money spread– Buy one in-the-money call, sell two at-the-money calls, and buy

one out-of-the-money call

Range Forward

Combination of two option positions– Buy an out-of-the money put and sell an out-of-

the money call of the same size• Purchase of put is financed by sale of call• Sell upside potential with call• Obtain downside risk protection with put• Cost of hedging is reduced

– Known as cylinder

The InternetInvestments Online

www.cboe.com/productswww.cboe.com//institutional/flex.htmlwww.finance.wat.ch/cbt/optionswww.optionmax.com